灰色Verhulst模型的样条插值函数的残差修正

本用样条函数对灰色Verhulst模型的残差序列进行插值拟合，然后作用于二阶线性微分方程，并以此修正原模型，得到一种新的预测模型的数值解，提高了拟合的精确度。     

高锰酸盐指数的灰色GM(1,1)预测

以中山市岐江河近7年的高锰酸盐指数监测数据为基础，采用灰色系统理论中的预测方法，建立了岐江河高锰酸盐指数的灰色预测模型。用该模型预测岐江河2006年、2007年、2008年高锰酸盐指数的值分别为5．3，5．4和5．4。     

色谱灰色数模的建立及其应用研究(Ⅰ)──连续GM(1,N)模型的建立及色谱保留行为的预测

应用灰色系统理论和最小二乘原理，推导出连续GM（1，N）模型，并将该模型用于高效液相色谱中溶质保留行为的预测．研究了烷烃、烷基苯及对羟基苯甲酸酯等化合物的容量因子与流动相组成、容量因子与碳数、保留时间与温度、保留时间与碳数的关系，并建立了相应的数学模型，经验证，预测结果良好．     

A detailed insight into the optimization of plate and frame heat exchanger design by comparing old and new generation metaheuristics algorithms

The voluminous utilization and application of plate and frame heat exchangers (PFHE) in many industries has accelerated the consumer and designer both to optimize exchanger total cost. Over the last few years, several old and new generation algorithms were employed and exploited to optimize PFHE cost. This study explores the application and performance of three new-generation algorithms Big Bang-Big Crunch (BBBC), Grey Wolf Optimizer (GWO), and Water Evaporation Optimization (WEO) in designing optimally PFHE. Besides, this study also compares the performance of three well-established old generations algorithms namely genetic algorithm (genetics and natural selection), particle swarm optimization (animals behaviour), and differential evolution (population-based) with the above three new algorithms in the optimization of PFHE.Seven design factors are chosen for PFHE optimization: exchanger length on hot and cold sides, height and thickness of fin, length of the fin-strip, fin frequency, and the number of hot side layers. The applicability of the suggested algorithms is assessed using a case study based on published research. Though DE performs the best in this study of design optimization concerning total cost and computational time, the three new-generation meta-heuristic algorithms BBBC, GWO, and WEO also provide the novel scope of application in heat exchanger design optimization and successfully finding the cost of the heat exchanger. According to this study, capital costs increase by 19.5% for BBBC, 24% for GWO, and 7.6% for GWO, but operational costs fall by 9.5% for BBBC and GWO when compared to the best performing algorithm (DE). On the other hand, WEO shows an increase of 32.6% in operational costs. Aside from that, a full analysis of the computing time for each algorithm is also provided. The DE has the quickest run time of 0.09 ?s, while the PSO takes the longest at 33.97 ?s. The rest of the algorithms have nearly identical values. As a result, a good comparison is established in this study, offering an excellent platform for designers and customers to make selections. Additionally, the three new generations algorithms mentioned here were not used earlier for optimization of PFHE and the comparative study illustrates that each of them possesses eat potential for cost optimization and also solving other complex problems.     

Grey relational analysis for optimization of wear parameters and surface roughness on nano composite coating

The higher wear resistance of Ni based nano composite coatings makes them potential replacement in protecting the substrate materials. The role of surface roughness of the coating along with wear parameters on the specific wear rate, pin temperature, and COF are addressed in the present study. The use of hard nano Al₂O₃ particles found significant role in increasing the resistance to wear for Ni matrix coatings on Al6061 material. The resistance to dislocation offered by these nano Al₂O₃ particles and smear out of debris with plastic deformation indicated abrasive and adhesive nature of wear mechanism in combination. The optimization of wear parameters are carried out by surface response method based grey relation analysis. The normal load applied onto the pin has significant influence on the specific wear rate and temperature rise in the pin. The surface roughness of the coating has also found instrumental in the higher pin temperature and friction coefficient.     

Combining grey relation and TOPSIS concepts for selecting an expatriate host country

As international corporate activities increase, their staffing involves more strategic concerns. However, foreign assignments have many differences, and dissatisfaction with the host country is a known cause of expatriate failure. From the point of view of an expatriate candidate, the decision of whether to take an expatriate assignment can be regarded as a FMCDM (fuzzy multiple criteria decision making) problem. This paper describes a fuzzy AHP (fuzzy analytic hierarchy process) to determine the weighting of subjective judgments. Using the Sugeno integral for λ-fuzzy measure, and using the nonadditive fuzzy integral technique to evaluate the synthetic utility values of the alternatives and the fuzzy weights, then the best host country alternative can be derived with the grey relation model. The authors further combine the grey relation model based on the concepts of TOPSIS (technique for order preference by similarity to ideal solution) to evaluate and select the best alternative. A real case of expatriate assignment decision-making was used to demonstrate that the grey relation model combined with the ideas of TOPSIS results in a satisfactory and effective evaluation.     

Bird mating optimizer: An optimization algorithm inspired by bird mating strategies

Thanks to their simplicity and flexibility, evolutionary algorithms (EAs) have attracted significant attention to tackle complex optimization problems. The underlying idea behind all EAs is the same and they differ only in technical details. In this paper, we propose a novel version of EAs, bird mating optimizer (BMO), for continuous optimization problems which is inspired by mating strategies of bird species during mating season. BMO imitates the behavior of bird species metaphorically to breed broods with superior genes for designing optimum searching techniques. On a large set of unimodal and multimodal benchmark functions, BMO represents a competitive performance to other EAs.     

非线性灰色微分方程(dx)/(dt)+ax~(■a)=b 的拟合

本文给出了拟合非线性灰色微分方程 dx/dt+ax~(■a)=b 的计算方法,并讨论了它的性质及应用.     

ITS示范工程对城市交通畅通性的贡献率研究

通过分析城市交通畅通性的影响因素及其与ITS(智能交通系统)的关系,挖掘ITS对城市交通畅通性的贡献率指标.搜集实证研究对象数据,采用灰色预测模型预测贡献率指标的数值,将ITS示范工程实施前后的数值进行对比,计算得到ITS示范工程对城市交通畅通性的贡献率.由贡献率结果判断ITS示范工程对城市交通畅通性的作用及ITS示范工程的实施效果如何,为未来ITS的发展提供相应的参考建议.     

Application of fuzzy soft set in decision making problems based on grey theory

There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems.